Bayesian Poisson common factor model with overdispersion for mortality forecasting in multiple populations

Abstract

This article presents a Poisson common factor model with an overdispersion factor to predict some multiple populations’ mortality rates. We use Bayesian data analysis and an extension of the Hamiltonian Monte Carlo sampler to compute the estimation of the model parameters and mortality rates prediction. We apply the proposed model to the real mortality data of some European countries. Using some model selection measures, we compare the proposed model with a log-linear model and those introduced in Antonio, Bardoutsos, and Ouburg (2015, Bayesian Poisson log-bilinear models for mortality projections with multiple populations. European Actuarial Journal 5 (2)(2) $$m_x:=\frac{q_x}{{\int }_0^{1}P(T_x>u)\mathrm{d}u}=\frac{{\int }_0^1{}_u{p}_x {\mu }_{x+u} \mathrm{d}u}{{\int }_0^1{}_u{p}_x \mathrm{d}u},$$(2) : 245–281) and Wong, Forster, and Smith (2018, Bayesian mortality forecasting with overdispersion. Insurance: Mathematics and Economics 83: 206–221).

Keywords:

• Bayesian analysis
• Hamiltonian Monte Carlo
• Lee-Carter mortality model
• Mixed Poisson distribution

Acknowledgements

The authors would like to thank the reviewer for his/her valuable comments and suggestions, which definitely improved the quality and presentation of the article.

Notes

1 See, www.mortality.org

2 For Austria, West Germany, England and Wales, Ireland, and Italy, the data is available until 2017